The Physics of the Vicsek Model

Abstract

In these lecture notes, prepared for the Microswimmers Summer School 2015 at Forschungszentrum Juelich, I discuss the well known Vicsek model for collective motion and its main properties. In particular, I discuss its algorithmical implementation and the basic properties of its universality class. I present results from numerical simulations and insist on the role played by symmetries and conservation laws. Analytical arguments are presented in an accessible and simplified way, but ample references are given for more advanced readings.

References in corpus (11)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Collective motion of self-propelled particles interacting without cohesion
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Pattern formation in self-propelled particles with density-dependent motility
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• The Role of Projection in the Control of Bird Flocks
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Comment on ``Phase Transitions in Systems of Self-Propelled Agents and Related Network Models''
• Active Brownian Rods

Cited by in corpus (86)

• Colloquium: Criticality and dynamical scaling in living systems
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
• A review of active matter reviews
• Giant fluctuations and structural effects in a flocking epithelium
• Emergent collective behavior of active Brownian particles by visual perception
• Effects of heterogeneous social interactions on flocking dynamics
• Finite-size scaling at the edge of disorder in a time-delay Vicsek model
• Marginal speed confinement resolves the conflict between correlation and control in natural flocks of birds
• Hydrodynamic Theory of Flocking in the Presence of Quenched Disorder
• Emergent vortices and phase separation in systems of chiral active particles with dipolar interactions
• Active Brownian Rods
• Time-reversal symmetry violations and entropy production in field theories of polar active matter
• Hard core run and tumble particles on a one dimensional lattice
• Small Obstacle in a Large Polar Flock
• Scale-free behavioral cascades and effective leadership in schooling fish
• Collective behavior of Vicsek particles without and with obstacles
• Designing, Synthesizing and Modeling Active Fluids
• Flocking and reorientation transition in the 4-state active Potts model
• Flocking with a $q$-fold discrete symmetry: band-to-lane transition in the active Potts model
• Anomalous fluctuations in homogeneous fluid phase of active Brownian particles
• The escape problem for active particles confined to a disc
• A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks
• Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
• Milling and meandering: Flocking dynamics of stochastically interacting agents with a field of view
• Self-propelled Vicsek particles at low speed and low density
• Epidemic processes on self-propelled particles: continuum and agent-based modelling
• Dominating Lengthscales of Zebrafish Collective Behaviour
• Giant number fluctuations in dry active polar fluids: A shocking analogy with lightning rods
• Signal propagation and linear response in the delay Vicsek model
• Vicsek Model by Time-Interlaced Compression: a Dynamical Computable Information Density
• Microscopic field theory for structure formation in systems of self-propelled particles with generic torques
• Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
• Emergent complex phases in a discrete flocking model with reciprocal and non-reciprocal interactions
• Collective olfactory search in a turbulent environment
• Noise induced swarming of active particles
• Equilibrium to off-equilibrium crossover in homogeneous active matter
• Taming Lagrangian Chaos with Multi-Objective Reinforcement Learning
• Data-driven model construction for anisotropic dynamics of active matter
• Clustering and anisotropic correlated percolation in polar flocks
• Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles
• Optimal collision avoidance in swarms of active Brownian particles
• Active XY model on a substrate: Density fluctuations and phase ordering
• Toward Task Capable Active Matter: Learning to Avoid Clogging in Confined Collectives via Collisions
• Swarming bottom feeders: Flocking at solid-liquid interfaces
• Lyapunov exponent in the Vicsek model
• Alignment Destabilizes Crystal Orders in Active Systems
• Detecting and characterizing phase transitions in active matter using entropy
• Short-time dynamics in active systems: the Vicsek model
• Scalar model of flocking dynamics on complex social networks
• Phase transitions on a class of generalized Vicsek-like models of collective motion
• Lifetime distributions for adjacency relationships in a Vicsek model
• Local interactions in active matter are reinforced by spatial structure
• Hydrodynamic theory of flocking at a solid-liquid interface: long range order and giant number fluctuations
• The collective motion of self-propelled particles affected by the spatial-dependent noise
• Data-driven assessment of optimal spatiotemporal resolutions for information extraction in noisy time series data
• AMEP: The Active Matter Evaluation Package for Python
• Aggregation of self-propelled particles with sensitivity to local order
• Three-state active lattice gas: a discrete Vicseklike model with excluded volume
• Emergent States in Systems of Chiral Self-Propelled Rods
• Vicsek Model Meets DBSCAN: Cluster Phases in the Vicsek Model
• Experimental and numerical study of a second-order transition in the behavior of confined self-propelled particles
• Active Matter Flocking via Predictive Alignment
• Initial perturbations dependence of non-equilibrium continuous and discontinuous pattern transition
• Optimal flock formation induced by agent heterogeneity
• The BKT Transition and its Dynamics in a Spin Fluid
• Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model
• Transient phases in the Vicsek model of flocking
• Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability
• Reduced density fluctuations via anti-aligning in active matter
• Flocking dynamics mediated by weighted social networks
• Braided mixing in confined chiral active matter
• Stability of discrete-symmetry flocks: sandwich state, traveling domains and motility-induced pinning
• Persistent exclusion process with time-periodic drive
• Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction
• Algebraic correlations and anomalous fluctuations in ordered flocks of Janus particles fueled by an AC electric field
• A renormalization group study of the dynamics of active membranes: universality classes and scaling laws
• On-lattice Vicsek model in confined geometries
• Invariance of velocity angles and flocking in the Inertial Spin model
• Phases and homogeneous ordered states in alignment-based self-propelled particle models
• The Inertial Spin Model of flocking with position-dependent forces
• Information conduction and convection in noiseless Vicsek flocks
• Quantifying Influence and Information Transfer in a Modified Vicsek Model with Non-reciprocal Interactions
• Waveform Proportionality and Taylor's Law Induced by Synchronization of Periodic and Chaotic Oscillators
• Anonymous leadership and stochastic resonance in collectives of self-propelled robots
• Confinement-induced collective motion in suspensions of run-and-tumble particles